Related papers: Fully Dynamic Spectral Sparsification of Hypergrap…
The diameter of a graph is one if its most important parameters, being used in many real-word applications. In particular, the diameter dictates how fast information can spread throughout data and communication networks. Thus, it is a…
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of…
In cut sparsification, all cuts of a hypergraph $H=(V,E,w)$ are approximated within $1\pm\epsilon$ factor by a small hypergraph $H'$. This widely applied method was generalized recently to a setting where the cost of cutting each hyperedge…
Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
A seminal palette sparsification result of Assadi, Chen, and Khanna states that in every $n$-vertex graph of maximum degree $\Delta$, sampling $\Theta(\log n)$ colors per vertex from $\{1, \ldots, \Delta+1\}$ almost certainly allows for a…
As a generalization of the use of graphs to describe pairwise interactions, simplicial complexes can be used to model higher-order interactions between three or more objects in complex systems. There has been a recent surge in activity for…
A cut $\varepsilon$-sparsifier of a weighted graph $G$ is a re-weighted subgraph of $G$ of (quasi)linear size that preserves the size of all cuts up to a multiplicative factor of $\varepsilon$. Since their introduction by Bencz\'ur and…
We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus few extra edges. A simple…
Time-evolving large graph has received attention due to their participation in real-world applications such as social networks and PageRank calculation. It is necessary to partition a large-scale dynamic graph in a streaming manner to…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
Graph Neural Networks (GNNs) have demonstrated superior performance across various graph learning tasks but face significant computational challenges when applied to large-scale graphs. One effective approach to mitigate these challenges is…
We analyze the spectral properties of the high-dimensional random geometric graph $G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever…
We study signals that are sparse in graph spectral domain and develop explicit algorithms to reconstruct the support set as well as partial components from samples on few vertices of the graph. The number of required samples is independent…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in…
We present techniques for maintaining subgraph frequencies in a dynamic graph, using data structures that are parameterized in terms of h, the h-index of the graph. Our methods extend previous results of Eppstein and Spiro for maintaining…
Graph Neural Network (GNN) achieves great success for node-level and graph-level tasks via encoding meaningful topological structures of networks in various domains, ranging from social to biological networks. However, repeated aggregation…
Graphs naturally lend themselves to model the complexities of Hyperspectral Image (HSI) data as well as to serve as semi-supervised classifiers by propagating given labels among nearest neighbours. In this work, we present a novel framework…